Given:
The vertices of the rectangle ABCD are A(-3,4), B(-1,4), C(-1,-1) and D(-3,-1).
It is reflected over the line x=2.
To find:
The vertices of the image A'B'C'D'.
Solution:
If a figure is reflected over the line x=a, then
[tex](x,y)\to (-(x-a)+a,y)[/tex]
[tex](x,y)\to (-x+a+a,y)[/tex]
[tex](x,y)\to (-x+2a,y)[/tex]
The rectangle ABCD is reflected over the line x=2. So, the rule of reflection is
[tex](x,y)\to (-x+2(2),y)[/tex]
[tex](x,y)\to (-x+4,y)[/tex]
Using this rule, we get
[tex]A(-3,4)\to A'(-(-3)+4,4)[/tex]
[tex]A(-3,4)\to A'(3+4,4)[/tex]
[tex]A(-3,4)\to A'(7,4)[/tex]
Similarly,
[tex]B(-1,4)\to B'(5,4)[/tex]
[tex]C(-1,-1)\to C'(5,-1)[/tex]
[tex]D(-3,-1)\to D'(7,-1)[/tex]
The vertices of image are A'(7,4), B'(5,4), C'(5,-1) and D'(7,-1).
Note: All options are incorrect or not in proper format.
The plan for a city park shows that the park is a quadrilateral with straight paths along the diagonals. For what values of the variables is the park a parallelogram? In this case, what are the values of x and y?
Picture relating to question has been attached below
Answer:
x = 10 ; y = 15
Step-by-step explanation:
The values for which the park is a parallelogram :
For the quadrilateral to be a parallelogram ; the diagonals will bisect each other such as :
VT = RV and UV = VS
From the diagram :
VT = 3x + 5y
RV = 6x + 3y
UV = 11y + 33 m
VS = 14y - 12 m
VT = RV and UV = VS
3x + 5y = 6x + 3y
3x - 6x = 3y - 5y
-3x = - 2y
3x = 2y
11y + 33 = 14y - 12
11y - 14y = - 12 - 33
-3y = - 45
y = 45/3
y = 15
From ;
3x = 2y
3x = 2*15
3x = 30
x = 30/3
x = 10
The two basic kinds of rulers are______
Find the slope of the line between the points (2, - 9) and (-8, – 99).
Answer: use desmos to graph them
Step-by-step explanation:
Write an equation to represent the problems below and solve for the missing value:
a) Keith has $15 more than Jay. If Keith has $87, how much money does Jay have?
(Let j represent the amount of money Jay has)
Answer:
poop=pee
Step-by-step explanation:
plzzz guys help I'm so confused
At the beginning of a population study, a city had 320,000 people. Each year since, the population has grown by 4.8%. Let t be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and t.
Answer:
y = 320,000 ( 1.048 ) ^x
x = number of years
(the ^ before the x symbolizes "to the power of," but I can't do that on my keyboard)
Step-by-step explanation:
formula i used:
A = amount that you start with
t = amount of years / time
%increase: you must convert your percent (4.8%) to a decimal (0.048)
A ( 1 + %increase ) ^t
Answer:
y = 320,000(1.048)^t
Step-by-step explanation:
4.8% = 0.048.
The population grows by 1.048 per year.
The required equation is:
y = 320,000(1.048)^t
Gil is reading a book that has 276 pages. on Monday, he read some pages, On Tuesday, he read twice as many pages than Monday. He plans to read 180 pages on Wednesday to finish the book.
variable-
equation-
justification-
What is the mean absolute deviation? With these numbers.
2, 8, 10, 12.
Please help :)
Step-by-step explanation:
jejnddndmkkdksjsjdenekekeej
Answer:
i think the answer is 3 I dont know if i'm right tho
Step-by-step explanation:
^-^ sorry if this is wrong but for me i did 3 on edge 2021
Whoever answer this question with explanation gets marked the brainiest
Step-by-step explanation:
Classroom A has n students.
Since Classroom B has 4 less students, they have (n - 4) students.
Also Classroom C has double the students in B, so they have 2(n - 4) students.
We have A + B + C = 40.
=> n + (n - 4) + 2(n - 4) = 40
=> n + n - 4 + 2n - 8 = 40
=> 4n - 12 = 40
=> 4n = 52, n = 13.
Hence there are 13 students in Classroom A.
My son takes trumpet lessons. He has a choice of plans. Plan A requires that he pay a $210 annual fee and then pay $10 for a lesson. Plan B does not have a fee, but you pay $25 for a lesson. Write an equation to find out for how many lessons Plan A would equal Plan B if x = number of lessons?
Answer:
10x + 210 = 25x
Step-by-step explanation:
Plan A
Annual fee = $210
Payment per lesson = $10
If 'x' lessons to be taken, total cost = 10x + 210
Plan B
Annual fee = 0
Payment per lesson = $25
Total cost for 'x' lessons = $25x
Equation for the equal payments in both the plans for 'x' lessons,
10x + 210 = 25x
A truck is carrying cranberry juice, grape juice, and pineapple juice bottles in a ratio of
7 : 2 : 3. If there are 40 grape juice bottles, then how many juice bottles in total are there?
Answer:
140
Step-by-step explanation:
7- Cranberry
2:Grape = 40 so 40/2 = 1
3:Pineapple
1= 20 juices
7+2+3 is 12
20 x 12 is 140
y= 3x +5
Who looks better
evaluate. (5.2 + 3) × (6.4 - 1.4)
What is true about the dilation?
On a coordinate plane, the image rectangle has points (0, 0), (0, 8), (9, 8), (8, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), (3, 0).
It is a reduction with a scale factor between 0 and 1.
It is a reduction with a scale factor greater than 1.
It is an enlargement with a scale factor between 0 and 1.
It is an enlargement with a scale factor greater than 1.
answer my question pls
Answer:
The answer is D.Step-by-step explanation:
This is because only a reduction can be 0-1, as it will shrink, while if you multiply a number by a number greater than 1, is will largen.
The dilation is an enlargement with a scale factor greater than 1. Thus, the correct option is D.
How does dilation affect length, area, and volume of an object?(SCALING ZOOMING SIMILAR FIGURES)
Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.
So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:
L = k × M
where 'k' will be called as scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.
So area of first figure = k² × area of second figure
Similarly, Volume of first figure = k³ × volume of second figure.
It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.
As it can be seen in the image below that the red rectangle is the pre-image therefore, it is the original figure.
The blue rectangle is the image of the original figure.
Now, as it can be seen that the pre-image is a smaller rectangle, while the image is a large rectangle, therefore, the dilation made is of enlargement.
Also, it can be observed that the ratio of any corresponding sides of the two rectangles is more than 1.
Hence, the dilation is an enlargement with a scale factor greater than 1. Thus, the correct option is D.
Learn more about Dilation:
https://brainly.com/question/27212783
#SPJ2
Math - Ratios
In one month, Jillian made 36 local phone calls and 20 long distance calls.
What was her ratio of local calls to long distance calls for that month?
A - 9 : 4
B - 2 : 1
C - 9 : 5
D - 3 : 2
which linear inequality is represented by the graph? O y<2/3x+3 (A)
O y>3/2x+3 (B)
O y>2/3x+3 (C)
O y<3/2x+3 (D)
Answer:
C y>2/3x+3
Step-by-step explanation:
Use y=mx+b format. The B is the y-intercept. From the y-intercept (3), go up two then to the right 3. That gives you the slope, or mx which is 2/3. The area shaded is above so it would be the greater than symbol.
45 point question Help Asap pic below Math
Answer:
i think 5
Step-by-step explanation:
Need help it’s really hard
Given:
[tex]OA=3[/tex] units
[tex]OA'=9[/tex] units
To find:
The scale factor of the dilation.
Solution:
From the given figure it is clear that the center of dilation is point O. Point A' is the image of point A. So,
[tex]\text{Scale factor}=\dfrac{OA'}{OA}[/tex]
Putting the given values, we get
[tex]\text{Scale factor}=\dfrac{9}{3}[/tex]
[tex]\text{Scale factor}=3[/tex]
Therefore, the scale factor of the dilation is 3.
Which expression shows another way to write 36+16?
419) + 4
4(9+4)
6(6+8)
(6+4)(6+4)
Answer please.............
Answer:
Option D: 1 is the correct answer.
Step-by-step explanation:
Given that:
n(x) = 7x+4
n(x) = 11
Putting n(x) = 11 in first function.
11 = 7x + 4
Now, we will subtract 4 from both sides
11 - 4 = 7x + 4 - 4
7 = 7x
7x = 7
Dividing both sides by 7
[tex]\frac{7x}{7}=\frac{7}{7}[/tex]
x = 1
Hence,
Option D: 1 is the correct answer.
PLEASE HELP!!!!!!!!!!!!!
Answer:
A
Step-by-step explanation:
A
What is the image point of (-7,7) after a translation right 1 unit and down 3 units?
Answer:
(-6, 4)
Step-by-step explanation
translation rule: (x+1,y-3)
(-7+1, 7-3)
(-6, 4)
pam buys the following items: a shirt that costs 11.99, pants that cost 23.98, and a belt that costs 9.95. she has a coupon for 20% off the entire purchase. About how much will the three items cost?
Answer:
$9.18
Step-by-step explanation:
45.92/20%
=$9.18
Answer:
47
Step-by-step explanation:
~It's ~ me ~ again ~ can ~ you ~ help ~ me ~ out ~ once ~ again?~
A circular disc has a diameter of 24 centimeters. What is the area of the disc?
Help!!! I need this ASAP!!!!
Answer:
im not too sure but i think the answer is c
Step-by-step explanation:
Help me pleaseee! Thank you! :)
Answer:
C.) 32
Step-by-step explanation:
2^5 = 32
Please help this is due tosay
Skyla wants to buy a massage table to start her spa business. She sees one she wants for $1,200. If she can save $13 a week, how many weeks will it take her to save up for the massage table?
Answer:
27 because you have to multipli and then divide
Answer:
about 93 weeks
Step-by-step explanation:
divide 1200 by 13 to get your answer which is 92.3076923077 so then you just instead of rounding to 92 you would round to 93 because it would take her more then 92 weeks so the answer would be about 93 weeks
What is the Slope of the line containing points Q(-4,-1) and T(0, 9)?
Answer:
kisses -A
Step-by-step explanation:
Answer: 5/2
Step-by-step explanation: Use the slope formula
Given △ABC with coordinates A(1, 3), B(4, 5), and C(5, 2), what are the coordinates of △AʹBʹCʹ after the glide reflection described by T⟨−1, 1⟩° Ry-axis?
Answer:
A' = ( 0,4 )
B' = ( -3,6 )
C' = ( -4,3 )
Step-by-step explanation:
Transformation involves changing the coordinates of a shape.
The coordinates of △ABC after the glide transformation are [tex]A' = ( 0,4 )[/tex], [tex]B' = ( -3,6 )[/tex] and [tex]C' = ( -4,3 )[/tex]
The coordinates of triangle ABC is given as:
[tex]A = (1,3)[/tex]
[tex]B = (4,5)[/tex]
[tex]C = (5,2)[/tex]
The glide reflection is given as: T⟨−1, 1⟩° Ry-axis
So, we start by translating the shape by (x - 1, y + 1).
The coordinate ABC becomes
[tex]A = (1 - 1, 3 + 1) = (0,4)[/tex]
[tex]B = (4 - 1, 5 + 1) = (3,6)[/tex]
[tex]C = (5 - 1, 2 + 1) = (4,3)[/tex]
Next, we reflect the coordinates across the y-axis.
The rule of this reflection is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]A' = ( 0,4 )[/tex]
[tex]B' = ( -3,6 )[/tex]
[tex]C' = ( -4,3 )[/tex]
Read more about transformation at:
https://brainly.com/question/1616371
Please help me would be very appreciated.
Answer:
C
Step-by-step explanation: